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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 15:58:16 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/05/t14571935083j7jdm1pw3ws4ic.htm/, Retrieved Sat, 27 Apr 2024 07:17:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293497, Retrieved Sat, 27 Apr 2024 07:17:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-05 15:58:16] [9b4dafad127b39cd929ee42874de7246] [Current]
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Dataseries X:
113149
112534
108783
106640
102617
102191
117359
116083
108666
105017
100918
103907
105732
103409
100255
97036
94055
92523
106380
104846
101411
98072
95678
99148
106813
106782
103496
100854
99592
98923
110497
114783
113551
112376
111683
113467
117277
117442
115640
114872
111628
111098
124301
125847
125323
122394
121164
123963
130549
128563
125418
121982
117708
116905
128862
129655
128649
126084
123725
123974




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293497&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293497&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293497&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean112037.4833333331339.1568942000183.6627013747051
Geometric Mean111564.867958075
Harmonic Mean111092.939748423
Quadratic Mean112508.687672182
Winsorized Mean ( 1 / 20 )112048.1166666671329.6569701407584.2684385393068
Winsorized Mean ( 2 / 20 )112075.7833333331311.8856907476885.4310586080548
Winsorized Mean ( 3 / 20 )112133.0333333331295.6801339781786.5437621467944
Winsorized Mean ( 4 / 20 )112196.3666666671281.1652665031887.5736874859995
Winsorized Mean ( 5 / 20 )112060.71225.6460997169791.4298997287045
Winsorized Mean ( 6 / 20 )112059.51217.0057057602992.0780399546227
Winsorized Mean ( 7 / 20 )112061.251198.2457362414993.5210922189468
Winsorized Mean ( 8 / 20 )112136.9833333331180.5121010039594.9901176260438
Winsorized Mean ( 9 / 20 )112073.5333333331136.8359462232298.5837347118226
Winsorized Mean ( 10 / 20 )112029.71125.1802194129699.5660055759329
Winsorized Mean ( 11 / 20 )112118.0666666671109.86159794424101.019863084135
Winsorized Mean ( 12 / 20 )112226.4666666671076.15754797347104.28442088057
Winsorized Mean ( 13 / 20 )112030.3833333331010.36140932486110.881494779372
Winsorized Mean ( 14 / 20 )112119.05964.938943481344116.192895682594
Winsorized Mean ( 15 / 20 )111936.3926.614620830431120.801353101555
Winsorized Mean ( 16 / 20 )111124.3763.249137154594145.593744677227
Winsorized Mean ( 17 / 20 )111314.983333333710.349704397535156.704483220335
Winsorized Mean ( 18 / 20 )111341.383333333698.818668676079159.328003563887
Winsorized Mean ( 19 / 20 )111541.833333333660.764001464127168.80737008399
Winsorized Mean ( 20 / 20 )111633.833333333610.715023265504182.792020959998
Trimmed Mean ( 1 / 20 )112054.7758620691304.3877683100385.9060308479032
Trimmed Mean ( 2 / 20 )112061.9107142861272.9907109557988.0304229636892
Trimmed Mean ( 3 / 20 )112054.2037037041245.604114046989.9597251165508
Trimmed Mean ( 4 / 20 )112023.8846153851218.8031975175291.9130215965607
Trimmed Mean ( 5 / 20 )111972.141190.2949276133494.0709209141263
Trimmed Mean ( 6 / 20 )1119501172.5504041850995.4756397681722
Trimmed Mean ( 7 / 20 )111926.1956521741151.4898732228897.201198425572
Trimmed Mean ( 8 / 20 )111899.8863636361128.7332369082599.1375842445684
Trimmed Mean ( 9 / 20 )111857.5476190481102.9004660884101.421253375445
Trimmed Mean ( 10 / 20 )111821.551079.7237336289103.56496436748
Trimmed Mean ( 11 / 20 )111788.6842105261050.65268687066106.399275048242
Trimmed Mean ( 12 / 20 )111738.7777777781014.20183811228110.174103002766
Trimmed Mean ( 13 / 20 )111667.058823529972.454077146556114.830161596104
Trimmed Mean ( 14 / 20 )111614.65625933.245503918137119.598386256775
Trimmed Mean ( 15 / 20 )111542.6889.923940441044125.339475578913
Trimmed Mean ( 16 / 20 )111486.357142857838.556282030628132.950357098136
Trimmed Mean ( 17 / 20 )111538.576923077818.417933808087136.285597267022
Trimmed Mean ( 18 / 20 )111571.458333333802.744619313989138.987488235898
Trimmed Mean ( 19 / 20 )111606.318181818777.420683685151143.559748954426
Trimmed Mean ( 20 / 20 )111616.5747.906884508183149.238497882525
Median112029.5
Midrange111536
Midmean - Weighted Average at Xnp111280.225806452
Midmean - Weighted Average at X(n+1)p111542.6
Midmean - Empirical Distribution Function111280.225806452
Midmean - Empirical Distribution Function - Averaging111542.6
Midmean - Empirical Distribution Function - Interpolation111542.6
Midmean - Closest Observation111280.225806452
Midmean - True Basic - Statistics Graphics Toolkit111542.6
Midmean - MS Excel (old versions)111614.65625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 112037.483333333 & 1339.15689420001 & 83.6627013747051 \tabularnewline
Geometric Mean & 111564.867958075 &  &  \tabularnewline
Harmonic Mean & 111092.939748423 &  &  \tabularnewline
Quadratic Mean & 112508.687672182 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 112048.116666667 & 1329.65697014075 & 84.2684385393068 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 112075.783333333 & 1311.88569074768 & 85.4310586080548 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 112133.033333333 & 1295.68013397817 & 86.5437621467944 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 112196.366666667 & 1281.16526650318 & 87.5736874859995 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 112060.7 & 1225.64609971697 & 91.4298997287045 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 112059.5 & 1217.00570576029 & 92.0780399546227 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 112061.25 & 1198.24573624149 & 93.5210922189468 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 112136.983333333 & 1180.51210100395 & 94.9901176260438 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 112073.533333333 & 1136.83594622322 & 98.5837347118226 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 112029.7 & 1125.18021941296 & 99.5660055759329 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 112118.066666667 & 1109.86159794424 & 101.019863084135 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 112226.466666667 & 1076.15754797347 & 104.28442088057 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 112030.383333333 & 1010.36140932486 & 110.881494779372 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 112119.05 & 964.938943481344 & 116.192895682594 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111936.3 & 926.614620830431 & 120.801353101555 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111124.3 & 763.249137154594 & 145.593744677227 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 111314.983333333 & 710.349704397535 & 156.704483220335 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 111341.383333333 & 698.818668676079 & 159.328003563887 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 111541.833333333 & 660.764001464127 & 168.80737008399 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 111633.833333333 & 610.715023265504 & 182.792020959998 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 112054.775862069 & 1304.38776831003 & 85.9060308479032 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 112061.910714286 & 1272.99071095579 & 88.0304229636892 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 112054.203703704 & 1245.6041140469 & 89.9597251165508 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 112023.884615385 & 1218.80319751752 & 91.9130215965607 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111972.14 & 1190.29492761334 & 94.0709209141263 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111950 & 1172.55040418509 & 95.4756397681722 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111926.195652174 & 1151.48987322288 & 97.201198425572 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111899.886363636 & 1128.73323690825 & 99.1375842445684 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111857.547619048 & 1102.9004660884 & 101.421253375445 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 111821.55 & 1079.7237336289 & 103.56496436748 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 111788.684210526 & 1050.65268687066 & 106.399275048242 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 111738.777777778 & 1014.20183811228 & 110.174103002766 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111667.058823529 & 972.454077146556 & 114.830161596104 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 111614.65625 & 933.245503918137 & 119.598386256775 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111542.6 & 889.923940441044 & 125.339475578913 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111486.357142857 & 838.556282030628 & 132.950357098136 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 111538.576923077 & 818.417933808087 & 136.285597267022 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 111571.458333333 & 802.744619313989 & 138.987488235898 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 111606.318181818 & 777.420683685151 & 143.559748954426 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 111616.5 & 747.906884508183 & 149.238497882525 \tabularnewline
Median & 112029.5 &  &  \tabularnewline
Midrange & 111536 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111280.225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111542.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111280.225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111542.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111542.6 &  &  \tabularnewline
Midmean - Closest Observation & 111280.225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111542.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111614.65625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293497&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]112037.483333333[/C][C]1339.15689420001[/C][C]83.6627013747051[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111564.867958075[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111092.939748423[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]112508.687672182[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]112048.116666667[/C][C]1329.65697014075[/C][C]84.2684385393068[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]112075.783333333[/C][C]1311.88569074768[/C][C]85.4310586080548[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]112133.033333333[/C][C]1295.68013397817[/C][C]86.5437621467944[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]112196.366666667[/C][C]1281.16526650318[/C][C]87.5736874859995[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]112060.7[/C][C]1225.64609971697[/C][C]91.4298997287045[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]112059.5[/C][C]1217.00570576029[/C][C]92.0780399546227[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]112061.25[/C][C]1198.24573624149[/C][C]93.5210922189468[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]112136.983333333[/C][C]1180.51210100395[/C][C]94.9901176260438[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]112073.533333333[/C][C]1136.83594622322[/C][C]98.5837347118226[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]112029.7[/C][C]1125.18021941296[/C][C]99.5660055759329[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]112118.066666667[/C][C]1109.86159794424[/C][C]101.019863084135[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]112226.466666667[/C][C]1076.15754797347[/C][C]104.28442088057[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]112030.383333333[/C][C]1010.36140932486[/C][C]110.881494779372[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]112119.05[/C][C]964.938943481344[/C][C]116.192895682594[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111936.3[/C][C]926.614620830431[/C][C]120.801353101555[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111124.3[/C][C]763.249137154594[/C][C]145.593744677227[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]111314.983333333[/C][C]710.349704397535[/C][C]156.704483220335[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]111341.383333333[/C][C]698.818668676079[/C][C]159.328003563887[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]111541.833333333[/C][C]660.764001464127[/C][C]168.80737008399[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]111633.833333333[/C][C]610.715023265504[/C][C]182.792020959998[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]112054.775862069[/C][C]1304.38776831003[/C][C]85.9060308479032[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]112061.910714286[/C][C]1272.99071095579[/C][C]88.0304229636892[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]112054.203703704[/C][C]1245.6041140469[/C][C]89.9597251165508[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]112023.884615385[/C][C]1218.80319751752[/C][C]91.9130215965607[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111972.14[/C][C]1190.29492761334[/C][C]94.0709209141263[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111950[/C][C]1172.55040418509[/C][C]95.4756397681722[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111926.195652174[/C][C]1151.48987322288[/C][C]97.201198425572[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111899.886363636[/C][C]1128.73323690825[/C][C]99.1375842445684[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111857.547619048[/C][C]1102.9004660884[/C][C]101.421253375445[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]111821.55[/C][C]1079.7237336289[/C][C]103.56496436748[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]111788.684210526[/C][C]1050.65268687066[/C][C]106.399275048242[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]111738.777777778[/C][C]1014.20183811228[/C][C]110.174103002766[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111667.058823529[/C][C]972.454077146556[/C][C]114.830161596104[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]111614.65625[/C][C]933.245503918137[/C][C]119.598386256775[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111542.6[/C][C]889.923940441044[/C][C]125.339475578913[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111486.357142857[/C][C]838.556282030628[/C][C]132.950357098136[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]111538.576923077[/C][C]818.417933808087[/C][C]136.285597267022[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]111571.458333333[/C][C]802.744619313989[/C][C]138.987488235898[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]111606.318181818[/C][C]777.420683685151[/C][C]143.559748954426[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]111616.5[/C][C]747.906884508183[/C][C]149.238497882525[/C][/ROW]
[ROW][C]Median[/C][C]112029.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111536[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111280.225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111542.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111280.225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111542.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111542.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111280.225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111542.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111614.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293497&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293497&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean112037.4833333331339.1568942000183.6627013747051
Geometric Mean111564.867958075
Harmonic Mean111092.939748423
Quadratic Mean112508.687672182
Winsorized Mean ( 1 / 20 )112048.1166666671329.6569701407584.2684385393068
Winsorized Mean ( 2 / 20 )112075.7833333331311.8856907476885.4310586080548
Winsorized Mean ( 3 / 20 )112133.0333333331295.6801339781786.5437621467944
Winsorized Mean ( 4 / 20 )112196.3666666671281.1652665031887.5736874859995
Winsorized Mean ( 5 / 20 )112060.71225.6460997169791.4298997287045
Winsorized Mean ( 6 / 20 )112059.51217.0057057602992.0780399546227
Winsorized Mean ( 7 / 20 )112061.251198.2457362414993.5210922189468
Winsorized Mean ( 8 / 20 )112136.9833333331180.5121010039594.9901176260438
Winsorized Mean ( 9 / 20 )112073.5333333331136.8359462232298.5837347118226
Winsorized Mean ( 10 / 20 )112029.71125.1802194129699.5660055759329
Winsorized Mean ( 11 / 20 )112118.0666666671109.86159794424101.019863084135
Winsorized Mean ( 12 / 20 )112226.4666666671076.15754797347104.28442088057
Winsorized Mean ( 13 / 20 )112030.3833333331010.36140932486110.881494779372
Winsorized Mean ( 14 / 20 )112119.05964.938943481344116.192895682594
Winsorized Mean ( 15 / 20 )111936.3926.614620830431120.801353101555
Winsorized Mean ( 16 / 20 )111124.3763.249137154594145.593744677227
Winsorized Mean ( 17 / 20 )111314.983333333710.349704397535156.704483220335
Winsorized Mean ( 18 / 20 )111341.383333333698.818668676079159.328003563887
Winsorized Mean ( 19 / 20 )111541.833333333660.764001464127168.80737008399
Winsorized Mean ( 20 / 20 )111633.833333333610.715023265504182.792020959998
Trimmed Mean ( 1 / 20 )112054.7758620691304.3877683100385.9060308479032
Trimmed Mean ( 2 / 20 )112061.9107142861272.9907109557988.0304229636892
Trimmed Mean ( 3 / 20 )112054.2037037041245.604114046989.9597251165508
Trimmed Mean ( 4 / 20 )112023.8846153851218.8031975175291.9130215965607
Trimmed Mean ( 5 / 20 )111972.141190.2949276133494.0709209141263
Trimmed Mean ( 6 / 20 )1119501172.5504041850995.4756397681722
Trimmed Mean ( 7 / 20 )111926.1956521741151.4898732228897.201198425572
Trimmed Mean ( 8 / 20 )111899.8863636361128.7332369082599.1375842445684
Trimmed Mean ( 9 / 20 )111857.5476190481102.9004660884101.421253375445
Trimmed Mean ( 10 / 20 )111821.551079.7237336289103.56496436748
Trimmed Mean ( 11 / 20 )111788.6842105261050.65268687066106.399275048242
Trimmed Mean ( 12 / 20 )111738.7777777781014.20183811228110.174103002766
Trimmed Mean ( 13 / 20 )111667.058823529972.454077146556114.830161596104
Trimmed Mean ( 14 / 20 )111614.65625933.245503918137119.598386256775
Trimmed Mean ( 15 / 20 )111542.6889.923940441044125.339475578913
Trimmed Mean ( 16 / 20 )111486.357142857838.556282030628132.950357098136
Trimmed Mean ( 17 / 20 )111538.576923077818.417933808087136.285597267022
Trimmed Mean ( 18 / 20 )111571.458333333802.744619313989138.987488235898
Trimmed Mean ( 19 / 20 )111606.318181818777.420683685151143.559748954426
Trimmed Mean ( 20 / 20 )111616.5747.906884508183149.238497882525
Median112029.5
Midrange111536
Midmean - Weighted Average at Xnp111280.225806452
Midmean - Weighted Average at X(n+1)p111542.6
Midmean - Empirical Distribution Function111280.225806452
Midmean - Empirical Distribution Function - Averaging111542.6
Midmean - Empirical Distribution Function - Interpolation111542.6
Midmean - Closest Observation111280.225806452
Midmean - True Basic - Statistics Graphics Toolkit111542.6
Midmean - MS Excel (old versions)111614.65625
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')